Thank you @KevinW.

Two questions to satisfy my academic mind...

(1) at what distance does it start to matter?

It would depend on your application but the cable length would need to be

significant in comparison with the wavelength of the signal when

propagating through the cable. At the maximum audio frequency likely to be

of interest - say 20 KHz, the wavelength, given a little reduction for the

velocity factor of the transmission line, is still going to be at least

10km, so line lengths of hundreds of metres would certainly suffer no real

issues from reflections due to mismatch.

(2) When you say the idea is for the input impedance to be so high that it

has no effect on the circuit, my understanding from the math is that as

you raise the load impedance, you're essentially tweaking the circuit

voltage too. For example, when source and load impedances match, the

circuit voltage is exactly half of the source voltage. But as you raise

the load impedance past that maximum power transfer point, the circuit

voltage continues to approach the maximum output voltage of the source.

So, is the idea of a 1 mega-ohm load virtually guarantee maximum voltage

since, in most cases, it will probably take up 99% of the total circuit

impedance?

Yes, that's the idea. The measured voltage tends towards the "open

circuit" voltage of your source. By loading the circuit with only a high

impedance, you can observe its operation with an oscilloscope without

modifying its behaviour by doing so. Incidentally, if 1M ohm is not

enough, you can switch to a "10x" probe and hit 10 M ohms at the cost of a

tenfold reduction in sensitivity.

As has also been pointed out, however, usually, when a generator specifies

its output impedance as 600 ohms (or 50 ohms, some are switchable) the

calibrated output voltage assumes it has been terminated with that

impedance. For this reason, your high impedance oscilloscope will probably

measure a level 6db higher unless you add a termination.

(3 -- extra credit): The input on my scope says 1 mega-ohm and 20 pF.

What's the reactance effect of the 20 pF and the net effect on load

impedance?

The 20pF indicates that there is a capacitive reactance component in

parallel with the scope's input impedance, so as you go higher in

frequency, the capacitive reactance tends to lower the input impedance. To

that you must also add the capacitance in any connecting cable and probe.

The reactance at 20pF hits about 400k ohms at 20 KHz, so it's starting to

become significant there...

When using 'scopes well into the megahertz it becomes the dominant

component of the input impedance.

Best Regards

Kevin